Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Linear Algebra Vector Spaces
Let S and T be non-empty subsets of ℝ2, and W be a non-zero proper subspace of ℝ2. Consider the following statements:
I. If span(S) = ℝ2, then span(S ∩ W) = W.
II. span(S ∪ T) = span(S) ∪ span(T).
Then
1
both I and II are TRUE
2
I is TRUE but II is FALSE
3
II is TRUE but I is FALSE
4
both I and II are FALSE